Topographic organization of eye-position dependent gain fields in human visual cortex

The ability to move has introduced animals with the problem of sensory ambiguity: the position of an external stimulus could change over time because the stimulus moved, or because the animal moved its receptors. This ambiguity can be resolved with a change in neural response gain as a function of receptor orientation. Here, we developed an encoding model to capture gain modulation of visual responses in high field (7 T) fMRI data. We characterized population eye-position dependent gain fields (pEGF). The information contained in the pEGFs allowed us to reconstruct eye positions over time across the visual hierarchy. We discovered a systematic distribution of pEGF centers: pEGF centers shift from contra- to ipsilateral following pRF eccentricity. Such a topographical organization suggests that signals beyond pure retinotopy are accessible early in the visual hierarchy, providing the potential to solve sensory ambiguity and optimize sensory processing information for functionally relevant behavior.


S U P P L E M E N T A R Y I N F O R M A T I O N T o p o g r a p h i c o r g a n i z a t i o n o f e y e -p o s i t i o n d e p e n d e n t g a i n f i e l d s i n h u m a n v i s u a l c o r t e x
. Change in the variance explained (R 2 ) of BOLD responses in the eye-movement task by the pRF-only model (optimized for stimulus configuration, right boxes) compared to the pRF model not optimized for stimulus configuration (left boxes). For each pair of boxes, the left box represents the R 2 of the model that did not include the peripheral elements, the right box represents the R 2 of the model where the peripheral elements were modelled with full contrast for a period of 500 ms after saccade offset (pRF-only model). In the box plots, the center is the median, the box bounds are Q1 and Q3, the whiskers extend to the highest/lowest values with a max/min of 1.5× the IQR, data beyond these limits are shown as points. Grey lines and points represent single participants (N = 11). R 2 is computed as the median over all voxels of the most visually responsive voxels (i.e. the same as for Figure 3B). Asterisks indicate a significant difference (see all test results in Supplementary Information -Statistics Output -1.). Overall, the pRF-only model yielded an increase in R 2 of approximately 0.035 in V1, V2, IPS0-1, IPS2-3-4 and TO1-2, compared to the pRF model not optimized for stimulus configuration.
*Additional explanation We considered four scenarios (see Methods -Simulation 1: left-over retinotopic input for details): 1) Blue: time-series were generated from both pRFs and pEGFs. The retinotopic representation of the visual input included the peripheral elements both when simulating the time-series and when estimating the pEGF parameters. This scenario follows the assumptions we make in our encoding model. 2) Red: time-series were generated from only the pRFs. The retinotopic representation included the peripheral elements when simulating the time-series, but not when estimating the pEGF parameters. This scenario captures reconstruction from leftover retinotopic activity. 3) Yellow: time-series were generated from only the pRFs. The retinotopic representation did not include the peripheral elements when simulating the time-series but did include them when estimating pEGF parameters. This scenario explores how well eye position can be reconstructed in case our stimulus model includes an excess of retinotopic elements. 4) Green: time-series were generated from both the pRFs and pEGFs. The retinotopic representation included the peripheral elements when simulating the time-series, but not when estimating the pEGF parameters. This scenario shows how well eye position can be reconstructed in case there is unaccounted retinotopic stimulation but gain fields do contribute to the time-series. In all simulated scenarios except scenario 2 (red), eye position reconstruction was above chance level. In scenario 2 (red), reconstruction was at chance level, indicating that accurate reconstruction from only left-over retinotopic activity is unlikely. However, scenario 3 (yellow) also leads to above chance level reconstruction, even though there were no pEGFs simulated. It is thus possible that our reconstruction did not rely on the existence of pEGFs but on a faulty retinotopic representation, that included an excess of peripheral elements. Still, reconstruction quality in the yellow scenario was significantly lower than in the blue scenario, which captures our two assumptions: that the peripheral elements are part of the visual input and that the gain of visual responses is modulated by eye position. In addition, results from the green scenario show that as long as pEGFs are real, omitting the peripheral elements should not hamper the reconstruction of eye position; there is no significant difference between the blue and green scenarios. To test whether our reconstruction results from the actual data might arise from a faulty stimulus model that includes too many peripheral elements (like is the yellow scenario), we re-estimated pEGF parameters using a retinotopic representation wherein the contrast of the peripheral elements was kept at 0 all the time. If the reconstruction quality would drop to chance level, we would know our data are unlikely to be driven by pEGFs, because the drop to chance level would be similar to the difference between the yellow and red scenario. However, if reconstruction quality would stay the same, it is more likely that our data are driven by pEGFs (like the blue and green scenarios). In panel C, the reconstruction quality for both versions of the retinotopic representation is displayed. Reconstruction quality is not significantly different between the two representations (F(1,10) = 1.61, p = 0.23).Together, the results from this simulation and the results from the real data in panel C indicate that the observed reconstruction most likely results from pEGFs truly affecting the measured BOLD time-series.  (3) Green ( where correlation is the Fisher transformed average of the two components (X and Y). We bootstrapped the model estimates 10 6 times to obtain 95%-confidence intervals (corrected for multiple tests with Bonferroni's correction; see table below). In the box plot, the center is the median, the box bounds are Q1 and Q3, the whiskers extend to the highest/lowest values with a max/min of 1.5× the IQR, data beyond these limits are shown as points. The difference between the simulated and estimated pEGF X0 is due to the structure of our modelling framework. B. Average pEGF X0 per over pRF eccentricity. The relationship between pRF eccentricity and pEGF X0 does not show the inversion that is observed in the data. C. Like A, but in this simulation the pEGF was omitted entirely. D. Like B. Also, when the pEGFs are omitted entirely from the simulation, the inversion of pEGF center with pRF eccentricity does not emerge.  Confidence intervals of the changes in R 2 per ROI. Estimates are derived by bootstrapping mdl1 100000 times using the "bootMer" and "confint" functions from the "boot" package in R. Estimates are corrected for multiple comparisons using Bonferroni's correction, by adjusting the limits of the confidence interval by the number of comparisons (= 10). I.e. the limits of a two-sided 95%-confidence interval become the (2.5/10=) 0.25 th percentile and (100-2.5/10) = 99.75 th percentile. Significance is determined by whether or not 0 is included in the confidence interval.

Supplementary Note 4. Linear mixed-effects model of average correlation between actual and reconstructed eye position components per ROI
Linear mixed-effects model of the average Fisher transformed Pearson correlations coefficients of the two reconstructed eye position components with the actual eye position per ROI.

Supplementary Note 7. PEGF center inversion
The horizontal component of the pEGF center (X0) appeared to shift with pRF eccentricity from being contralateral to ipsilateral. We quantified the inversion point per ROI and visual field by estimating the linear relationship between pRF eccentricity and pEGF X0. We computed two least-squares solutions, one for pRFs in the left, and one for pRFs in the right visual hemifield. Using the coefficients of these least-squares solutions, we computed where the two lines would intersect. If they did not intersect after 0 (i.e. in case of parallel or diverging lines), the intersection was set to 'NA'. We computed the median across the visual ROIs where we found an intersection point.
In addition to the pEGF parameter obtained with the optimal retinotopic representation of the visual input (i.e. where the contrast of the peripheral elements increased to 100% after saccade offset for 500 ms), we also computed the intersection after fitting the pEGFs using a retinotopic representation without any peripheral elements. In both cases the pEGF centers inverted from contralateral to ipsilateral (see Supplementary Figure 6B and S6C). The point of inversion was more central when the contrast of the peripheral elements increased to 100% (see table below). Based on the two different retinotopic representations, we expect the point of inversion to be approximately between 6 to 8 degrees from the fovea.